== Definitions and Introduction ==
As we mentioned before, the piano illustrates the basis for musical theory. This chapter discusses intervals in theory and shows the relationships between them. It also will give you a better understanding of how intervals can be used to derive remaining parts of chords you don't know. We will further discuss chords in a different section, but this will be a basic introduction in chord building, and will show you how you can accompany different songs while you play melodies with your right hand. In this section, things might begin to get really, really confusing, especially if you don't have any kind of previous music theory knowledge. Take your time, relax, and if any questions or ideas for improvements to this chapter arise just leave comments on the talk page. I will do my best to explain the concepts to you. It might be a good idea if you have already familiarized yourself with the scales, as i will be using them extensively during this chapter.
=== So, what are intervals? ===
An interval can be briefly described as the distance between two notes. For example, in the C major (Ionian) scale, the first and third finger when pressed at the same time form an interval (a major third). Note that notes in intervals can be separate and in order: ascending (c, e) and descending (e, c), or simultaneous (both notes played at the same time). Also note that intervals are characterized by the grades of the scale, taking each note of a scale and assigning it a number. Intervals are the basis to form chords.
== Key Concepts ==
=== Counting Notes ===
When calculating the distance between two notes, you must be really careful and count the semitones, which, on the piano, means both white and black keys. For example, after c comes c#, then d, then d#, etc. On the piano, the black keys represent semitones that are ignored (not played) when making a third major interval on the c scale. You can play the entire C major scale on just the white keys.
== Types of Intervals ==
=== Second and Third Intervals ===
The reason why these intervals are together in this section is because their theoretical explanation is exactly the same, and they work in the same way; the 4th, 5th and 8th intervals work differently.
==== Method for Counting Notes ====
Play a C and an E. If there are exactly 3 notes (3 black and white keys), without counting the initial and last note, in between them, the interval is called a third major. If there are two notes in between, the interval is called a third minor. The same concept applies to second minor and major. A second minor in the C scale is C and C# (no semitones are separating the notes). These second intervals, which, as seen later on, are used for improvisation techniques, are usually played separately and often quickly, and are repeated in ascending order. This method works only for second and third intervals from any given key. Note: Play these notes always in ascending order. The reason for this is that intervals change depending on the order sometimes. This will be discussed further on this chapter.
==== Alternative Methods ====
Although the method for counting notes described above starts to become really ineffective especially on greater intervals, many musicians prefer to sing the notes of the scale with numbers from 1 to 8 to identify the kind of interval that is played simultaneously by ear. If you count up to 3 notes for example, (C to E) the interval is quickly identified as a third major. If we approach a different method and lower the third note of the major scale (from E to Eb, or D#) the interval is minor. This is mainly why you need to know the major and minor scales by heart in order to play or identify given intervals. Scale recognition by ear is heavily based on the intervals that you hear, depending on the scales. I will be using this method for better clarity and understanding.
=== 6th and 7th Intervals ===
Taking of course the 1st and 6th grades of the A major scale, we can say that A and F# is a 6th interval. If we lower the F# to an F, it becomes a 6th minor. Same applies to the seventh interval: Taking the 1st and 6th grades of the D major scale, we can lower the C# and make the 7th interval a minor one.
=== 4th and 5th Intervals ===
Taking the 1st grades of the F major scale, we can have a 5th interval by playing F and C. This is denominated as a perfect 5th. If C is lowered to B, the interval is known as a diminished 5th or tritone; if C is shifted to C#, the interval is known as an augmented 5th. If we take the 1st and 4th grades of the G major scale, we would obtain a perfect 4th interval once G and C are played. Shifting C to C# would result in an augmented 4th; lowering C to B would result in a diminished 4th.
=== Octaves ===
Octaves are also said to be perfect or fixed, because the same note is played at a higher octave. The simultaneous playing of an octave is known as a doubled note. Play the middle C on the piano keyboard, then play the next C that you find either to the right or left of the middle C. Notice how the note sounds the same, or has the same feeling, but it sounds higher. Well, that is because it's the same note, just an octave above (to the right) or below (to the left).
== Relationships Between Intervals ==
Although it is not really necessary to review this, it helps to clear and avoid any confusion you might have. Remember the perfect 4th interval we had mentioned before? Well, you can find out that if we lower the C and play the notes G and B, we obtain a third major interval. Same when shifting the note: We obtain an augmented 4th interval or a diminished 5th interval. For the 2nd and 3rd interval relationships, a 3rd minor interval is also an augmented 2nd interval, and a 2nd major interval is a diminished third interval. This relationship also works with 6th and 7th intervals, and even with octaves, if you stop and think about. Now that we have discussed the intervals at length, let's make some decisions here.
== Determining the Kinds of Intervals ==
We have so far discussed what the types of intervals are and how to identify them. This section deals with when you don't know whether to name an interval perfect, diminished and augmented or major and minor. Just keep this in mind: When the same higher note is played an octave above and that note forms a 4th or 5th interval, the interval is denominated as perfect. So, if we take C and F, but we play the F note an octave higher, we get a perfect 11th interval. You can expand this all the way to even a 22nd or a 23rd interval, though only in really strange cases do intervals get this big, so there is usually no need to identify intervals that are higher than an octave or so. (An exception is montuno patterns. Montuno is a completely different style that deals with chord inversions played differently on each hand; therefore, this topic is not relevant to a discussion of intervals.)
== Introduction to the Formation of Chords ==
Hopefully you feel alright with we have discussed so far and understand most of the relationships between intervals. it is not really required that you so, but it would really help when you get to chord inversions and any other types of identification. Although this has really been based on musical theory, learning to play piano without music theory is like learning how to speak a language without proper grammar and syntax concepts. You also hopefully might have been playing and discovering some different intervals than the ones I already mentioned here. now, lets go to the construction of chords by using intervals.
=== Brief Explanation of Chords ===
A chord is 3 or more notes played together. If the notes are played separately, the "broken" chord is called an arpeggio. It is a good technical exercise and also a good improvisation technique if you manage to play arpeggios quickly. Chords are the basis or core for the accompaniment of all songs and are used differently into many styles. If we base the formation of chords into intervals we can say that a chord consists of two intervals being put together, as shown in the next section.
=== Major Chords ===
The reason why this is called a major chord is because of the first major interval as you will notice. Most chords are named after the first interval that you play. For the sake of making things easy to comprehend and play I base this type of chords on the c scale and put the notation of the fingers which are used after the note. So if we would play d with the index finger the notation used will be d2. I assume you are playing these chords with your right hand. if you wish to do so with the left hand, simply reverse the order of the fingers you use on your right hand. This is why piano builds a lot of coordination. Lets begin with a third major interval (c1 e3). Now that we have such kind of interval, we can add a minor second interval above by playing with the pinky the note g, thus making the interval with notes e g. First play it as an arpeggio and then play all the notes at the same time. If you know other scales, do the same and don't be afraid to experiment. Form a major third interval and then add an augmented second above the higher note of the third major interval.
=== Minor Chords ===
As you would have guessed, the minor third interval begins the chord (c1 eb3), then adding the g again, in which we get a third minor and then a third major. Notice how the order to intervals reverse. Major chord: Major third interval, minor third on top. Minor chord--minor first, followed by third major.
== Conclusion and Tips ==
Although this might seem really overwhelming at first, this uses the basis of interval and shows their importance into chord forming. it is good that you keep on experimenting and see what kind of intervals form which kind of chords. It is much better to discover the syntax of a language or learn the vocabulary with a dictionary of the same language rather than remind yourself of the equivalent word in your first language. In other words, using intervals on this manner will really help you see relationships between minor and major , chord inversions and figuring them out rather than try to remember the notes that compose them constantly. This will also make you a better pianist and a better musician. Explore, practice and put dedication into it. Once you practice chords there will be the need to no longer remember the chord's composition by using intervals. Piano can be as easy and as hard as you want it to be. IN the next chapters we will be discussing more chords and their intervals. Finally, we will focus on stylistic patterns used in many different rhythms. What makes piano really complex to introduce and teach fully most of the time is that the diversity is really great as far as the styles you can play and relations in music theory.